a. The point estimate for the population mean is b. The confidence interval at 80% is c. This means there is an 80% probability that the true mean of the population lies within the given confidence interval.
Response:
Option B is correct
Step-by-step breakdown:
(One-tailed test at a significance level of 5%)
n = 16 and x̄ = 1.97
s = 0.1
Standard error of the mean = 
Difference in means = 
t statistic = Difference in means/se = -1.2
degrees of freedom = 16 - 1 = 15
p-value = 0.124375
(B) do not reject the null hypothesis since the test statistic (-1.2) is > the critical value (-1.7531).
Class B exhibits the most consistent sleep patterns since there's a smaller variance between 6.87 and 3.65 compared to the other classes.
Answer with explanation: Given that Circle 1 has a center at (−4, −7) and a radius of 12 cm, while Circle 2's center is at (3, 4) with a radius of 15 cm. Two circles are similar if one can be transformed and scaled to fit over the other, creating identical circles. The circles qualify as similar because the transformation rule (x,y) → (x+7,y+11) can be applied to Circle 1, followed by dilation using a scale factor of 5/4. Since Circle 1's center is at (-4,-7), we translate it to (3,4) through (-4+7,-7+11). With Circle 1 having a radius of 12 and Circle 2 having 15 cm, we denote the scale factor as k.
Answer:
89
Step-by-step explanation:
Given that
2 O, 2 T and 1 M
Now based on this, the following arrangements exist
1
Three arrangements i.e. {M,T,O}
2
XX or XY
XX in 2C1 = two arrangements i.e. {OO or TT}
XY in 3C2 × 2! = six arrangements
3
XXY or XYZ
XXY in 2C1 × 2C1 × 3! ÷ 2! = twelve arrangements
XYZ in 3C3 × 3! = six arrangements
4
XXYY or XXYZ
XXYY = 4! ÷ (2! × 2!) = six arrangements
XXYZ in 2C1 × 4! ÷ 2! = twenty four arrangements
5
= 5! ÷ (2! ×2!)
= 120 ÷ 4
= 30
Thus, the overall total is
= 3 + (2 +6)+ (12 +6) + (6 +24) + 30
= 89
